Natural Convection over Two Superellipse Shapes with a Porous Cavity Populated by Nanofluid
The influences of superellipse shapes on natural convection in a horizontally subdivided non-Darcy porous cavity populated by Cu-water nanofluid are inspected in this paper. The impacts of the inner geometries <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" displa...
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| Format: | article |
| Language: | EN |
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MDPI AG
2021
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| Online Access: | https://doaj.org/article/c6e1ae26ac7b4c0db3441b788e53e9c4 |
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| Summary: | The influences of superellipse shapes on natural convection in a horizontally subdivided non-Darcy porous cavity populated by Cu-water nanofluid are inspected in this paper. The impacts of the inner geometries <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>n</mi><mo>=</mo><mn>0.5</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1.5</mn><mo>,</mo><mn>4</mn></mrow><mo>)</mo></mrow><mo>,</mo></mrow></semantics></math></inline-formula> Rayleigh number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msup><mrow><mn>10</mn></mrow><mn>3</mn></msup><mo>≤</mo><mi>R</mi><mi>a</mi><mo>≤</mo><msup><mrow><mn>10</mn></mrow><mn>6</mn></msup><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>, Darcy number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo stretchy="false">(</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>5</mn></mrow></msup><mo>≤</mo><mi>D</mi><mi>a</mi><mo>≤</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>, porosity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mn>0.2</mn><mo>≤</mo><mi>ϵ</mi><mo>≤</mo><mn>0.8</mn></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, and solid volume fraction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mn>0.01</mn><mo>≤</mo><mo>∅</mo><mo>≤</mo><mn>0.05</mn></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula> on nanofluid heat transport and streamlines were examined. The hot superellipse shapes were placed in the cavity’s bottom and top, while the adiabatic boundaries on the flat walls of the cavity were considered. The governing equations were numerically solved using the finite volume method (FVM). It was found that the movement of the nanofluid upsurged as Ra boosted. The temperature distributions in the cavity’s core had an inverse relationship with increasing Rayleigh number. An extra porous resistance at lower Darcy numbers limited the nanofluid’s movement within the porous layers. The mean Nusselt number decreased as the porous resistance increased <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mrow><mi>D</mi><mi>a</mi><mo>≤</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>4</mn></mrow></msup></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. The flow and temperature were strongly affected as the shape of the inner superellipse grew larger. |
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